Burhanuddin Rabbani's supporters carry a portrait of the former Afghan president and head of the government's peace council at a vigil outside his house in Kabul. Photograph: Omar Sobhani/Reuters

The Taliban have refused to accept or deny responsibility for the assassination in Kabul of former Afghan president Burhanuddin Rabbani, which has plunged the country into a deep political crisis.

On the first of three days of national mourning following the killing on Tuesday of Hamid Karzai's chief peace negotiator, the Taliban's spokesmen published a statement on their website refusing to discuss the incident and contesting an earlier report by the Reuters news agency that said the Taliban accepted responsibility.

"Our position on this issue is that we can't talk about it and all the media reports that claim responsibility are groundless," it said. "Right now we don't want to talk."

Their reticence to comment on the killing – by a man posing as a senior Taliban envoy with explosives hidden in his turban – is in stark contrast to the aftermath of other spectacular attacks in the capital: the Taliban's PR department often feeds details to the media while their operations are still ongoing.

Diplomats say it raises the possibility that Mullah Omar and other high-ranking Taliban leaders may not have approved, or even have been aware of, an operation conducted by a splinter or affiliated group linked to Pakistan's powerful military intelligence agency, the ISI, which has long-standing ties to militant groups.

A western expert on the Taliban, who did not want to be identified, said senior figures within the movement had tried to bypass the ISI and hold direct talks with Karzai's government and the US, and Pakistan had responded with ruthless efforts to reassert control of any negotiations.

He said spectacular attacks in Kabul in recent months were probably designed to derail any independent Taliban contacts with the government, while the killing of Rabbani could have been aimed at putting all talks on hold for several months.

"It is not that they want to close the door on one set of negotiations [with Rabbani] but on all kinds of negotiations," he said. "They would rather have no talks than some talks that they can't control."

Diplomats are bracing themselves for the possibility that blame will be pinned on the Haqqani network, a militant group that nominally follows Omar but is believed to be heavily influenced by the ISI. If the recent rhetoric of US ambassadors in the region is anything to go by, it is already in a state of apoplectic anger over Pakistan's role in supporting Haqqani, which has been blamed for several major attacks, including last week's 20-hour assault on the US embassy in Kabul.

That fury would grow if Haqqani was implicated in the hugely destabilising killing of Rabbani.

"There is no doubt that there is a very serious conspiracy by those opposed to peace talks," said Ahmed Rashid, an influential Pakistani commentator who strongly supports a political settlement in Afghanistan. "They are trying to sabotage them before they take off."

There was no love lost between Rabbani and the Taliban, a movement he fought against. And the Taliban have a stated policy of trying to kill members of the high peace council, the body that Rabbani chaired.

But some analysts think killing him would be a step too far, even for the Taliban. Wahid Mujda a political analyst who held a mid-level position within the old Taliban regime, said its Quetta Shura would be reluctant to claim credit for killing a figure who commanded respect among a large group of Afghans, not least among his fellow Tajiks.